1. Field of the Invention
The present invention relates to an X-ray CT apparatus and, more particularly, a technique for executing image reconstruction which can have both high spatial resolution on a trans-axial plane and excellent continuity along a body axis direction in a helical scan x-ray CT apparatus.
2. Description of the Prior Art
A scan system, etc. of an X-ray CT apparatus (abbreviated simply as "CT" hereinafter) which is used to take tomograms of a subject in the prior art will be explained in brief.
(1) Fan beam (single slice) X-ray CT PA1 Nview=view number per one time, PA1 Nch=channel number, PA1 .phi.=fan angle, PA1 .psi.=angle relative to channel, PA1 CentCH=center channel=(Nch+0.5)/2 (In the case of QQ offset fitting). PA1 .phi.:Nch=.psi.:(k-CentCH) and (180+2 .psi.):x=360: Nview (see FIG. 9) PA1 Nview=view number per one time, PA1 Nch=channel number, PA1 .phi.=fan angle, PA1 .psi.=angle relative to channel, PA1 CentCH=center channel=(Nch+0.5)/2 (In the case of QQ offset fitting).
First, a single slice CT will be explained.
As shown in FIG. 1, the main current of present CTs is the single slice CT which comprises an X-ray focus for generating a X-ray beam (continuous fan beam along a channel direction), and a detector composed of sectorial or linear N-channel (e.g., 1000 channel) detecting elements which are arranged in a line.
The single slice CT can acquire intensity data of X-ray passing through the subject (called as "projection data" hereinafter) while rotating a pair of the X-ray focus and a detector around the subject. Projection data are acquired Nview times, e.g., 1000 times per one rotation and then image reconstruction is carried out based on the projection data according to a method to be described later.
Data acquisition per one time is called as "one view", data detected by one detecting element or a detecting element group in one view is called as "one beam", and all beams (data detected by all detecting elements) in one view is called as "direct data" in a lump.
Next, the scan system of CT will be explained. A conventional scan and a helical scan are two representative types of such scan system.
A first scan system is the conventional scan shown in FIG. 2.
This system is a scan system in which an X-ray focus is rotated around a target plane (e.g. , plane A) by one rotation. In order to get images of plural planes (e.g., planes A and B), the CT first acquires data while rotating around the plane A by one rotation. Then, the plane B is set to a plane of rotation by moving either a patient couch on which the subject is laid down or the X-ray focus and the detector. Then, like the plane A, data are acquired while rotating around the plane shape B by one rotation.
Accordingly, in the conventional scan system, a scanning time becomes longer if a scanning range is broad in the body axis direction (Z-axis direction) of the subject or if a great number of target planes are needed.
A second scan system is the helical scan shown in FIG. 3.
In this system, while rotating continuously the X-ray focus and the detector and also moving the patient couch along a body axis direction of the subject synchronously with such rotation, the CT can acquire data. In other words, an X-ray focus orbit can scan helically around the subject. According to this scan system, a wide range can be scanned at high speed.
Where a coordinate system is defined as shown in FIG. 1. An XY plane corresponds to planes A, B to be scanned by the conventional scan, and a Z-axis direction is a body axis direction of the subject, which is called as a slice direction in the above single slice CT.
Next, an image reconstruction method will be explained. First of all, normal image reconstruction in the conventional scan system as the first scan system will be explained.
Such normal image reconstruction will be explained in brief with reference to FIG. 5 hereunder.
The conventional scan is made up of three following steps. Suppose that, as shown in FIG. 4, the subject only exists as an arrow signal indicating a center of rotation.
(i) Data acquisition and Correction
The CT executes first the conventional scan to acquire data. Normally, a rotation angle, though only shown partially, is 360.degree., 180.degree.+fan angle, etc. Projection data are shown in FIG. 5A. Raw data can be derived by correcting the projection data with regard to various factors such as sensitivity of the detector, X-ray intensity, etc.
(ii) Convolution Using Reconstruction Function
Convolution of the raw data of respective angles and reconstruction functions is performed. Such convolution data are shown in FIG. 5C. Neighborhood of originally existing signals are recessed shapes.
(iii) Back Projection Operation
Convolution data are added to all pixels on X-ray passing paths when the data are collected. FIG. 5B shows back projection operation at a certain angle. If such pack projection operation is repeated at necessary angles, only original signals remain.
Processes (ii) and (iii) explained above, if combined with each other, are called a filter correction back projection method (convolution back projection method, i.e., CBP method).
Next, an image reconstruction system which is able to achieve high resolution in the image reconstruction of the above conventional scan will be explained.
This is a system which can achieve improvement in spatial resolution and therefore is so-called QQ (Quarter-Quarter) process to improve the spatial resolution from 0.50 mm to 0.35 mm, for example.
An outline of the QQ process will be explained hereunder.
The QQ is such a method that, as described above, normal spatial resolution is about 0.5 mm but spatial resolution of an axial image is improved up to about 0.35 mm, for example.
An trans-axial plane (XY plane) viewed from the Z-axis direction is shown in FIG. 6A. Assuming that a field of view FOV (effective field-of-view diameter) is 500 mm and the channel number of the detector is 1000, spatial resolution of the axial image obtained by the normal image reconstruction of the above conventional scan is about 0.50 mm. In FIG. 6, FCD (Focus-Center-Distance) denotes a distance between the X-ray focus and the center of rotation, and FDD (Focus-Detector-Distance) denotes a distance between the X-ray focus and the detector.
FIG. 7 is a view showing an so-called QQ offset fitting state wherein the detector which is composed of even-numbered elements (channels) aligned along the channel direction is not fitted symmetrically about the center line, but such detector is fitted to have an offset of a 1/4 channel distance along the channel direction.
At this time, a path (indicated by an upward thick arrow) connecting a virtual k+0.5-th channel, which is located in the right middle between the k-th channel and the k+1-th channel in the j-th view, and the focus of the j-th view, as shown in FIG. 8A, coincides with a path (indicated by a downward thick arrow) connecting the focus of the j+x-th view and the y-th channel, as shown in FIG. 8B in which the detector is rotated by a half turn from FIG. 8A.
Hence, data of the y-th channel in the j+x view in FIG. 8B are data of the k+0.5 channel in the j-th view in FIG. 8A. Relationships among above j, k, x, y can be expressed by equations in the following. EQU y=CentCH.times.2-(k+0.5) EQU x={[(k+0.5-CentCH).times..phi.]/[Nch.times.180]+0.5}.times.Nview[Equation 1 ]
Where .phi.:Nch=.psi.:(k+0.5-CentCH) and (180+2 .psi.):x=360:Nview (see FIG. 9)
Accordingly, data of the virtual k+0.5 channel located between the k-th channel and the k+1-th channel can be derived from data of the y-th channel in the j+x-th view.
However, in the case of Nview=1000, Nch=1000, j=100, k=700, .phi. =50.degree. in the above equations, y=300 channel and x=555.625 can be obtained, which yields such data in the 655.255-th view.
Therefore, data T-Data can be derived by interpolating data D (655, 300) of the 300-th channel in the 655-th view and data D (656, 300) of the 300-th channel in the 656-th view based on an integer portion Ix=int(x)=655 according to the following equations. EQU T.Data=(1-w).times.D(Ix, y)+w.times.D(Ix+1, y) [Equation 2]
Ix=int(x), w=x-Ix, D(j, k): data of the k-th channel in the j-th view
Data called complementary beam (see a reference B0 in FIG. 8B and FIG. 16 to be described later) are selected as data of the k+0.5-th channel in the target j-th view.
Data (complementary beams) of 0.5-th, 1.5-th, 2.5-th, 3.5-th, . . . , k+0.5-th, . . . , 999.5-th virtual channels, corresponding to all detecting elements, in the j-th view can be obtained in the same way.
Total complementary beams of all channels are called as the complementary data. Since x becomes decimal in substantially all cases, respective complementary beams can be obtained by virtue of two data interpolation of one channel.times.two views.
This process is repeated to respective Nviews.
With the use of 2.times.Nch channel data having double sampling point number (double sampling density) compared to normal conventional scan obtained by the above process, image reconstruction can be performed by means of the convolution and the back projection.
Since complementary data have been obtained by virtue of two data interpolation as described above, spatial resolution does not reach twice but it reaches 1.4 times which corresponds to spatial resolution of about 0.35 mm.
Again, a conception of QQ will be explained with reference to FIGS. 10 and 11.
Data in the j-th view will be considered. As indicated by a reference M1 in FIG. 10, by placing alternately direct data, which are acquired in the j-th view and indicated by solid lines, and complementary data, which are acquired by virtue of interpolation of one channel.times.two views and indicated by dotted lines, image reconstruction can be effected as data which are collected by the high sampling density detector having twice detecting element number. In other words, as shown in FIG. 11, reconstruction can be accomplished with the use of high density data which is constructed by arranging alternately direct data on an orbit of the conventional scan around the Z-axis direction (body axis direction) and complementary data obtained by interpolation. Consequently, improvement in spatial resolution of the trans-axial plane can be attained.
At that time, since the scan system employs the conventional scan, slice positions of direct data and complementary data (sampling positions along the Z-axis direction) are the same.
Then, image reconstruction in the helical scan system as the second scan system will be explained hereunder.
When the conventional scan and the helical scan as two scan systems shown in FIGS. 2 and 3 are viewed from this side, states of scan systems are shown in FIGS. 12 and 13 respectively. Abscissas indicate a slice (Z-axis) direction and ordinates indicate rotation phase (angle) respectively. Sampling positions of respective data are represented by connecting by arrows. Such diagrams are called scan views hereinafter.
In the conventional scan shown in FIG. 12, necessary 360.degree. data corresponding to the above step (i) are collected on the target slice plane and thus, as described above, image reconstruction can be achieved via the steps (i).fwdarw.(ii).fwdarw.(iii).
On the contrary, in the helical scan shown in FIG. 13, since it is a helical scan, only one view can be collected on the target slice plane.
Therefore, after necessary data have been obtained by virtue of interpolation of raw data, which are obtained by correcting projection data being acquired, along the Z-axis direction in place of the step (i), image reconstruction must be effected by a filter correction back projection method for the above (ii).fwdarw.(iii).
In the case of the single slice CT, two representative interpolation methods in the helical scam system are a 360.degree. interpolation method and a complementary beam interpolation method.
First, the 360.degree. interpolation method will be explained with reference to the scan diagram in FIG. 14.
As shown in FIG. 14, the 360.degree. interpolation method is such a method that two direct data of two views, to which are positioned opposite mutually sandwiching the target slice position so as to make a closest pair and which have a same phase (projection angle), can be linearly interpolated to be in reciprocal proportion to the distance between the slice plane and each sampling position.
For instance, if the target slice position (Z-coordinate of the slice plane) is set to Z=Z0, data acquired at the slice position are only one view at the phase 0.degree.. Hence, for example, in order to obtain data at the phase .theta., upper direct data 1 and lower direct data 2 of the slice position are selected and then respective direct data are linearly interpolated every channel to be in reciprocal proportion to the distance (Z-coordinate) between each sampling Z-coordinate and the target slice position Z0, so that interpolation data can be obtained. This process is repeated to necessary phases.
Data in the j-th view in the 360.degree. interpolation method are shown in FIG. 19.
The 1, 2, 3, . . . , Nch data in the direct data 1 and the 1, 2, 3, . . . , Nch data in the direct data 2 are respectively interpolated to be in reciprocal proportion to the distance between the sampling position of the direct data 1/the direct data 2 and the target slice position, whereby interpolation data can be obtained.
Second, the complementary beam interpolation method will be explained.
The complementary beam interpolation method is such a method that interpolation is executed by using complementary data which is virtual data.
As shown in FIG. 16, the beams of acquired direct data which are directed to respective detecting elements, are indicated by solid line arrows, when the focus is positioned at a "black round mark" position. At this time, the left side beam 1 and the beam indicated by a dotted line acquired when the X-ray focus is positioned at a "white round mark" position pass through the same path. The beam from the "white round mark" is called complementary beam.
Similarly, the beam 2 and the beam indicated by a dotted line from a light gray mark (roughly dotted mark) are complementary beams to pass through the same path, and also the beam 3 and the beam indicated by a dotted line from a dark gray mark (finely dotted mark) are complementary beams to pass through the same path. In this manner, all beams from the "black round mark" have complementary beams.
Therefore, a method wherein virtual data (called the complementary data) can be formed by extracting the complementary beam corresponding to respective beams from data acquired at respective focus positions, i.e., white round mark-.fwdarw.light gray mark (roughly dotted mark)-.fwdarw.dark gray mark (finely dotted mark) and then linear interpolation is performed by use of the direct data and the complementary data is the complementary beam interpolation method.
At this time, the complementary beams can be given by following equations. EQU y=CentCH.times.2-k EQU x={[(k-CentCH).times..phi.]/[Nch.times.180 ]+1/2}.times.Nview[Equation 3]
Where
Accordingly, the virtual complementary data which is shifted by about half turn in the slice direction and passes through the same path as the k-th channel can be obtained from data of the y-th channel in the j+x-th view.
A difference from the above QQ reconstruction resides in that data of the virtual channel having the path sandwiched by channels of the direct data can be derived in the QQ (see FIG. 8) whereas data having the same path as channels of the direct data can be derived at this time (see FIG. 20).
In other words, an object of the complementary beam in the complementary beam interpolation of the helical scan in the prior art is to obtain the beam having the same path as the direct data.
However, for example, in the case of Nview=1000, Nch=1000, j=100, k=700, .phi.=50.degree. in the above equations, y=300.5 channel and x=555.4861 can be obtained, which yields such data of the 300.5-th channel in the 655.4861-th view.
Hence, complementary data T.Data can be derived by four-point interpolating data D (655, 300) of the 300-th channel and data D (655, 301) of the 301-th channel in the 655-th view and data D (656, 300) of the 300-th channel and data D (656, 301) of the 301-th channel in the 656-th view based on integer portions Ix=int(x)=655 and Iy=int(y)=300 according the following equations. Respective complementary beams can be obtained by virtue of four point interpolation of two channels.times.two views. EQU T.Data=(1-w).times.[D(Ix, Iy)+D(Ix, Iy+1)]/2 +w.times.[D(Ix+1, Iy)+D(Ix+1, Iy+1)]/2 [Equation 4 ]
Ix=int(x), w=x-Ix, Iy=int(y), D(j, k): data of the k-th channel in the j-th view
FIG. 18 is a conceptual view showing the complementary beam interpolation method applied to the j-th view data.
The 1, 2, 3, . . . , Nch direct data and the 1, 2, 3, . . . , Nch complementary data obtained by the above four-point interpolation are respectively interpolated by use of the direct data and the complementary data to be in reciprocal proportion to distances between the direct data/the complementary data and the target slice position, whereby interpolation data can be obtained.
Respective beams of the complementary data can be obtained from data in the different views as stated above. However, since the scan system is the helical scan, the slice position is shifted view after view. As a consequence, as shown in FIG. 18, the slice position of the complementary beam is shifted channel after channel.
Interpolation is executed by using respective data collected at the slice positions shifted by one turn in the 360.degree. interpolation method, whereas shift of the slice positions of the direct data and the complementary data is about half turn in the complementary beam interpolation method. Hence, the complementary beam interpolation method is superior in resolution along the slice direction to the 360.degree. interpolation method.
However, spatial resolution on the trans-axial plane is about 0.50 mm, which similar to that in the conventional scan system, in the 360.degree. interpolation method, whereas spatial resolution on the trans-axial plane is less than 0.50 mm in the complementary beam interpolation method since the complementary data can be obtained by virtue of four-point interpolation.
(2) Multi-slice X-ray CT
Next, scan and image reconstruction in a multi-slice CT will be explained hereunder.
In recent years, according to the request to take the tomograms of the subject with high precision at high speed over the broad range, as shown in FIGS. 21A, 21B, 21C respectively, the multi-slice CT which has plural detector columns such as two, four, eight columns has been proposed.
First, while taking a four-column multi-slice CT shown in FIG. 21B as an example, several terms will be explained.
FIG. 6A shows the geometry viewed from the Z -axis direction, and a circle in FIG. 6A shows an effective field-of-view FOV.
FIG. 6B shows a plane including the Z -axis, which is viewed from the direction perpendicular to the Z-axis. A thickness of the beam along the Z-axis direction (a distance FCD from the X-ray focus) is set as a basic slice thickness T when the X-ray incident from the X-ray focus to the detecting element passes through the center of rotation.
The helical scan system in the multi-slice CT has been set forth in following literatures 1 and 2.
Patent Application Publication (KOKAI) Hei 4-224736; "CT Apparatus" H. Aradate, K. Nanbu (filed on Dec. 25, 1990) . . . (Literature 1)
Where it is assumed that a helical pitch P in the multi-slice CT is set similarly to a product of the detector column number N and the basic slice thickness T, i.e., a total slice thickness at the center of rotation by expanding a conception of a basic pitch in the above single slice CT, as shown in Eq.(1) in the following. EQU P=N.times.T (1)
The helical pitch will be expressed by a value obtained by dividing the helical pitch by the basic slice thickness hereinbelow. The helical scan at the pitch 4 is expressed by Eq.(1).
One of the interpolation methods, which have been proposed in the above literature 1 and in which the subject is helically scanned at the pitch N by the N column multi-slice CT, is an expanded 360.degree. interpolation method in the single slice CT.
FIG. 22 is a scan diagram showing the above 360.degree. interpolation method in the four column multi-slice CT. Like the 360.degree. interpolation method in FIG. 14, interpolation is effected by use of two direct data which put the target slice position between them. This is temporarily called a "contiguous interpolation method", which has been set forth in the above literature 1.
In addition, in a following literature 2, three type methods for data processing in the helical scan system have been set forth.
Patent Application No. Hei 8-341739; "X-ray CT Apparatus", K. Taguchi, H. Aradate (filed on Dec. 20, 1996) . . . (Literature 2)
First, a high density sampling scan method (four columns are at Pitch=2.5, 3.5, 4.5 and two columns are at Pitch=1.5) has been disclosed.
In this method, the helical pitch has been set forth and also a method of improving the sampling density in the helical scan having the Pitch=2.5, 3.5, 4.5, etc. has been set forth.
Second, a new complementary beam interpolation method (interpolation method between the complementary beams) has been disclosed.
In other words, a method of utilizing the complementary beams has been recited. In this method, several combinations of an interpolation method using combinations of direct data/direct data and complementary data/complementary data and either the normal helical pitch or the helical pitch according to the high density sampling method have been set forth.
Third, a filter interpolation method has been disclosed.
In other words, as for the method of executing the filter interpolation process along the slice direction, four methods, i.e., a filter interpolation method 1 (filter interpolation method by using the sampling data filter process), a filter interpolation method 2 (filter interpolation method by using interpolation data/weighted addition (filter) process), a filter interpolation method 3 (filter interpolation method by using virtual scan raw data process), and a filter interpolation method 4 (filter interpolation method by using reconstruction voxel data process) have been set forth. In this method, combinations of the filter interpolation method and the normal helical pitch or the helical pitch at the high density sampling method, and further combinations of these and the new complementary beam interpolation method have been set forth.
However, there have been following problems in the prior art. More particularly, in the QQ in the above conventional scan system, the resolution of 0.35 mm can be derived on the trans-axial plane, but continuity along the slice direction is not good because of the conventional scan, so that the QQ method in the conventional scan system is not suitable for obtaining three dimensional volume data.
On the contrary, the interpolated image reconstruction in the helical scan system has good continuity along the body axis direction and is also suitable for obtaining three dimensional volume data. Especially the complementary beam interpolation method can obtain high spatial resolution along the body axis direction, but it has the spatial resolution on the trans-axial plane of less than 0.50 mm.